Question

Sunita and sumedha start travelling in the same direction at 8 km/hr and 13 km/hr respectively. After 4 hours, sunita doubled her speed and sumedha reduced her speed by 1 km/hr and reached the destination together. How long did the entire journey last?

Answer 1

Let length of journey is x km.

for Sunita,

speed of Sunita is 8 km/h

in 4 hours, distance travelled by Sunita = 8 × 4 = 32km

after that Sunita has to complete (x - 32)km with speed 2×8 = 16km/h .

so, time taken by Sunita to travel (x - 32)km = (x - 32)km/16km/h = (x - 32)/16 hours

for sumedha,

speed of sumedha is 13 km/h

in 4 hours, distance travelled by sumedha = 4 × 13 = 52km

after that sumedha has to travel (x - 52)km in (x - 32)/16 hours with speed (13 - 1) = 12km/h , if both reached the destination together.

so, (x - 52)/12 = (x - 32)/16

or, (x - 52)/3 = (x - 32)/4

or, 4x - 208 = 3x - 96

or, x = 208 - 96 = 112 km

so, total time = 4 + (x - 32)/16 = 4 + (112 -32)/16 = 4 + 5 = 9 hours.